Journal
MECHANICS OF TIME-DEPENDENT MATERIALS
Volume 20, Issue 2, Pages 175-195Publisher
SPRINGER
DOI: 10.1007/s11043-016-9290-3
Keywords
Real and complex order fractional derivatives; Constitutive equations; The Laplace transform; The Fourier transform; Thermodynamical restrictions
Funding
- Serbian Ministry of Science [174005, 174024]
- Provincial Secretariat for Science [114-451-1084]
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We introduce complex order fractional derivatives in models that describe viscoelastic materials. This cannot be carried out unrestrictedly, and therefore we derive, for the first time, real valued compatibility constraints, as well as physical constraints that lead to acceptable models. As a result, we introduce a new form of complex order fractional derivative. Also, we consider a fractional differential equation with complex derivatives, and study its solvability. Results obtained for stress relaxation and creep are illustrated by several numerical examples.
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